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Colombia Team Selection Test
2005 Colombia Team Selection Test
1
Colombia TST
Colombia TST
Source: unknown
June 7, 2005
Columbia
geometry
3D geometry
number theory proposed
number theory
Problem Statement
Let
a
,
b
,
c
a,b,c
a
,
b
,
c
be integers such that
a
b
+
b
c
+
c
a
=
3
\frac{a}{b}+\frac{b}{c}+\frac{c}{a}=3
b
a
+
c
b
+
a
c
=
3
prove that
a
b
c
abc
ab
c
is a perfect cube!
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